You should be standing for the Prayer After Communion.
The General Instruction of the Roman Missal has instructions on this in n. 43.
"43. The faithful should stand ... from the invitation, Orate, fraters (Pray, brethren), before the prayer over the offerings until the
end of Mass, except at the places indicated below. ... and, as circumstances allow, they may sit or kneel while the period of sacred silence after Communion is observed."
Clearly when the priest is saying the Prayer After Communion it is not the period of "sacred silence".
Another liturgical book that gives instructions about this is the Ceremonial of Bishops:
"166 When the bishop returns to the chair after the communion, he puts on the skullcap and, if need be, washes his hands. All are seated and a period of prayerful silence may follow, or a song of praise or a psalm may be sung.
167. Standing at the chair as a minister holds the book or after returning to the altar with the deacons, the bishop sings or says, Let us pray.
(Ceremonial of Bishops, Liturgical Press, 1989, ISBN 0-8146-1818-9, page 60.)
To look up the GIRM go to http://www.romanrite.com/girm.html